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An effective artificial neural network together with a genetic algorithm have been demonstrated for predicting the optimal thermal performance of plain plate-fin heat sinks in a ducted flow under multi-constraints such as pressure drop, mass, and space limitations. A series of constrained optimal designs can be efficiently performed. Comparisons of the optimal results between the artificial neural network with genetic algorithm (ANN-GA) and the response surface methodology with sequential quadratic programming (RSM-SQP) methods are made. Although more training patterns are needed for the ANN-GA method as compared to that for the RSM-SQP method, the ANN-GA method which has randomly uniform-distributed training patterns in the whole solving domain can be applied to the global region of interest, not just in the region of operability. Consequently, a globally precise optimal solution can be achieved with the ANN-GA method; while the solution obtained with the RSM-SQP method may cause a significant error if the optimal values of the design variables happen to be located beyond the region of operability.